\(CPT\) -Symmetric Universe

The simplest model that can accomodate a viable nonbaryonic dark matter candidate is the standard electroweak theory with the addition of right-handed or sterile neutrinos. We reexamine this model and find that the sterile neutrinos can be either hot, warm, or cold dark matter. Since their only direct coupling is to left-handed or active neutrinos, the most efficient production mechanism is via neutrino oscillations. If the production rate is always less than the expansion rate, then these neutrinos will never be in thermal equilibrium. However, enough of them may be produced so that they provide the missing mass necessary for closure. We consider a single generation of neutrino fields \(\left (\nu_L,\,\nu_R\right )\) with a Dirac mass, \(\mu\), and a Majorana mass for the right-handed components only, \(M\). For \(M\gg \mu\) we show that the number density of sterile neutrinos is proportional to \(\mu^2/M\) so that the energy density today is {\it independent of} \(M\). However \(M\) is crucial in determining the large scale structure of the Universe. In particular, \(M\simeq 0.1-1.0 {\rm ~keV}\) leads to warm dark matter and a structure formation scenario that may have some advantages over both the standard hot and cold dark matter scenarios.